Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12019 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#12904 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#106 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,32,34,44)(25,36)(26,29)(27,40)(28,33,41,46)(30,38)(31,39)(35,49,48,45)(37,50)(42,53,52,47)(43,51);(22,24,25,33,27,35,38,47,26,34,37,46,39,48,51,53)(23,28,30,32,31,42,36,45,29,41,43,44,40,52,50,49);(18,19,20,21)(23,29)(28,41)(30,43)(31,40)(32,44)(36,50)(42,52)(45,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5892);